We study two- and three-gluon glueballs of $C=+$ using the method of QCD sum rules. We systematically construct their interpolating currents, and find that all the spin-1 currents of $C=+$ vanish. This suggests that the ground-state spin-1 glueballs
of $C=+$ do not exist within the relativistic framework. We calculate masses of the two-gluon glueballs with $J^{PC} = 0^{pm+}/2^{pm+}$ and the three-gluon glueballs with $J^{PC} = 0^{pm+}/2^{pm+}$. We propose to search for the $J^{PC} = 0^{-+}/2^{-pm}/3^{pm-}$ three-gluon glueballs in their three-meson decay channels in future BESIII, GlueX, LHC, and PANDA experiments.
We use QCD sum rules to study mass spectra of $P$-wave charmed baryons of the $SU(3)$ flavor $mathbf{6}_F$. We also use light-cone sum rules to study their $S$- and $D$-wave decays into ground-state charmed baryons together with light pseudoscalar an
d vector mesons. We work within the framework of heavy quark effective theory, and we also consider the mixing effect. Our results can explain many excited charmed baryons as a whole, including the $Sigma_c(2800)^0$, $Xi_c(2923)^0$, $Xi_c(2939)^0$, $Xi_{c}(2965)^{0}$, $Omega_c(3000)^0$, $Omega_c(3050)^0$, $Omega_c(3066)^0$, $Omega_c(3090)^0$, and $Omega_c(3119)^0$. Their masses, mass splittings within the same multiplets, and decay properties are extracted for future experimental searches.
After examining the Feynman diagrams corresponding to the $bar D^{(*)} Sigma_c^{(*)}$, $bar D^{(*)} Lambda_c$, $D^{(*)} bar K^{*}$, and $D^{(*)} bar D^{(*)}$ hadronic molecular states, we propose a possible binding mechanism induced by shared light q
uarks. This mechanism is similar to the covalent bond in chemical molecules induced by shared electrons. We use the method of QCD sum rules to calculate its corresponding light-quark-exchange diagrams, and the obtained results indicate a model-independent hypothesis: the light-quark-exchange interaction is attractive when the shared light quarks are totally antisymmetric so that obey the Pauli principle. We build a toy model with four parameters to formulize this picture, and estimate binding energies of some possibly-existing covalent hadronic molecules. A unique feature of this picture is that binding energies of the $(I)J^P = (0)1^+$ $Dbar B^*/D^* bar B$ hadronic molecules are much larger than those of the $(I)J^P = (0)1^+$ $DD^*/bar B bar B^*$ ones, while the $(I)J^P = (1/2)1/2^+$ $bar D Sigma_c/bar D Sigma_b/B Sigma_c/B Sigma_b$ hadronic molecules have similar binding energies.
Inspired by the evidence of the odderon exchange recently observed by the D0 and TOTEM Collaborations, a QCD sum rule investigation is performed to study the odderon as a three-gluon bound state. There may exist six lowest-lying three-gluon odderons
with the quantum numbers $J^{PC} = 1/2/3^{pm-}$. We systematically construct their interpolating currents, and calculate their mass spectra. To verify their existence, we propose to search for the spin-3 odderons in their $VVV$ and $VVP$ decay channels directly at LHC, with $V$ and $P$ light vector and pseudoscalar mesons respectively.
There are eighteen possibly existing $D^{(*)} bar D^{(*)}$, $D^{(*)} bar K^{(*)}$, and $D^{(*)} D_s^{(*)-}$ hadronic molecular states. We construct their corresponding interpolating currents, and calculate their masses and decay constants using QCD s
um rules. Based on these results, we calculate their relative production rates in $B$ and $B^*$ decays through the current algebra, and calculate their relative branching ratios through the Fierz rearrangement, as summarized in Table III. Our results support the interpretations of the $X(3872)$, $Z_c(3900)$, $Z_c(4020)$, and $X_0(2900)$ as the molecular states $D bar D^*$ of $J^{PC} = 1^{++}$, $D bar D^*$ of $J^{PC} = 1^{+-}$, $D^* bar D^*$ of $J^{PC} = 1^{+-}$, and $D^* bar K^*$ of $J^P = 0^{+}$, respectively. Our results also suggest that the $Z_{cs}(3985)$, $Z_{cs}(4000)$, and $Z_{cs}(4220)$ are strange partners of the $X(3872)$, $Z_c(3900)$, and $Z_c(4020)$, respectively. In the calculations we estimate the lifetime of a weakly-coupled composite particle $A = |BCrangle$ to be $1/t_A approx 1/t_B + 1/t_C + Gamma_{A to BC} + cdots$, with $cdots$ partial widths of other possible decay channels.
There may exist seven $bar D^{(*)} Sigma_c^{(*)}$ hadronic molecular states. We construct their corresponding interpolating currents, and calculate their masses and decay constants using QCD sum rules. Based on these results, we calculate their relat
ive production rates in $Lambda_b^0$ decays through the current algebra, {it i.e.}, $mathcal{B}(Lambda_b^0 to P_c K^-):mathcal{B}(Lambda_b^0 to P_c^prime K^-)$ with $P_c$ and $P_c^prime$ two different states. We also study their decay properties through the Fierz rearrangement, and further calculate these ratios in the $J/psi p$ mass spectrum, {it i.e.}, $mathcal{B}(Lambda_b^0 to P_c K^- to J/psi p K^-):mathcal{B}(Lambda_b^0 to P_c^prime K^- to J/psi p K^-)$. Our results suggest that the $bar D^{*} Sigma_c^{*}$ molecular states of $J^P = 1/2^-$ and $3/2^-$ are possible to be observed in future experiments.
We study the $P_{cs}(4459)^0$ recently observed by LHCb using the method of QCD sum rules. Our results support its interpretation as the $bar D^* Xi_c$ hadronic molecular state of either $J^P=1/2^-$ or $3/2^-$. Within the hadronic molecular picture,
the three LHCb experiments observing $P_c$ and $P_{cs}$ states cite{lhcb,Aaij:2015tga,Aaij:2019vzc} can be well understood as a whole. This strongly supports the existence of hadronic molecules, whose studies can significantly improve our understanding on the construction of the subatomic world. To verify this picture, we propose to further investigate the $P_{cs}(4459)^0$ to examine whether it can be separated into two states, and to search for the $bar D Xi_c$ molecular state of $J^P=1/2^-$.
We study strong decays of the possible fully-charm tetraquarks recently observed by LHCb, and calculate their relative branching ratios through the Fierz rearrangement. Together with our previous QCD sum rule study [Phys. Lett. B 773, 247 (2017)], ou
r results suggest that the broad structure around $6.2$-$6.8$ GeV can be interpreted as an $S$-wave $ccbar c bar c$ tetraquark state with $J^{PC} = 0^{++}$ or $2^{++}$, and the narrow structure around 6.9 GeV can be interpreted as a $P$-wave one with $J^{PC} = 0^{-+}$ or $1^{-+}$. These structures were observed in the di-$J/psi$ invariant mass spectrum, and we propose to confirm them in the di-$eta_c$, $J/psi h_c$, $eta_c chi_{c0}$, and $eta_c chi_{c1}$ channels. We also propose to search for their partner states having the negative charge-conjugation parity in the $J/psi eta_c$, $J/psi chi_{c0}$, $J/psi chi_{c1}$, and $eta_c h_c$ channels.
The past seventeen years have witnessed tremendous progress on the experimental and theoretical explorations of the multiquark states. The hidden-charm and hidden-bottom multiquark systems were reviewed extensively in [Phys. Rept. 639 (2016) 1-121].
In this article, we shall update the experimental and theoretical efforts on the hidden heavy flavor multiquark systems in the past three years. Especially the LHCb collaboration not only confirmed the existence of the hidden-charm pentaquarks but also provided strong evidence of the molecular picture. Besides the well-known $XYZ$ and $P_c$ states, we shall discuss more interesting tetraquark and pentaquark systems either with one, two, three or even four heavy quarks. Some very intriguing states include the fully heavy exotic tetraquark states $QQbar Qbar Q$ and doubly heavy tetraquark states $QQbar q bar q$, where $Q$ is a heavy quark. The $QQbar Qbar Q$ states may be produced at LHC while the $QQbar q bar q$ system may be searched for at BelleII and LHCb. Moreover, we shall pay special attention to various theoretical schemes. We shall emphasize the model-independent predictions of various models which are truly/closely related to Quantum Chromodynamics (QCD). There have also accumulated many lattice QCD simulations through multiple channel scattering on the lattice in recent years, which provide deep insights into the underlying structure/dynamics of the $XYZ$ states. In terms of the recent $P_c$ states, the lattice simulations of the charmed baryon and anti-charmed meson scattering are badly needed. We shall also discuss some important states which may be searched for at BESIII, BelleII and LHCb in the coming years.
